6 Emma is in a park with her dog, Roxy. Emma throws a ball and Roxy catches it in her mouth. The ground in the park is horizontal. Emma throws the ball from a point at a height of 1.2 metres above the ground and Roxy catches the ball when it is at a height of 0.5 metres above the ground. Emma throws the ball with an initial velocity of \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal.

1. Find the time that the ball takes to travel from Emma's hand to Roxy's mouth.
2. Find the horizontal distance travelled by the ball during its flight.
3. During the flight, the speed of the ball is a maximum when it is at a height of \(h\) metres above the ground. Write down the value of \(h\).
4. Find the maximum speed of the ball during its flight.
   [0pt] [4 marks]
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